A Note on Star-Pr"ufer Extensions

Abstract

Let ★ be a star operation on a ring extension R \subseteq S . The ring extension R \subseteq S is said to be a ★-Pr¨ufer if R[p] \subseteq S is a Pr¨ufer extension for each ★-prime ideal p of R. We study properties of ★-Pr¨ufer extensions. In particular, we investigate the transfer of star-Pr¨ufer properties from the extension R \subseteq S to the extension R[X] \subseteq S [X] of polynomial rings, where X is an indeterminate over S .